A\:=\:\begin{pmatrix}-2&0&0\\ 1&-2&0\\ 0&1&-2\end{pmatrix}.\:a.\:Show\:that\:A\:has\:only\:one\:distinct\:eigen\:value.\:b.\:what\:is\:the\:geomteric\:multiplicity\:of\:this\:eigen\:value?\:c.\:Pick\:an\:eigen\:vector\:v_1\:for\:this\:eigen\:value.\:Find\:a\:generalized\:eigen\:vector\:of\:order\:2\:say\:v_2\:so\:that\:\left\{v_1,v_2\right\}is\:a\:basis\:for\:W_2\:_{\:the\:space\:of\:generalized\:eigen\:vectors\:of\:order\:2.}d.\:Find\:a\:vector\:v3\:that\:is\:a\:generalized\:eigen\:vector\:of\:order\:3\:so\:that\:\left\{v_1,v_2,v_3\right\}is\:a\:basis\:for\:the\:space\:of\:generalized\:eigenvectors.\:Form\:the\:matrix\:P\:with\:columns\:v_1,v_2,v_3.\:e.\:Find\:P^{-1}.f.\:Compute\:the\:Jordan\:decomposition\:A\:=\:S\:\:+\:N.\:g.\:Compute\:e^{tS}.\:h.\:Compute\:e^{tN}.i.\:Compute\:e^{tA}.\:Solve\:only\:using\:Linear\:Algebra..